Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 13650.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13650.c1 | 13650q2 | \([1, 1, 0, -6390825, -4664842875]\) | \(14779663816445754533/3745407876327936\) | \(7315249758453000000000\) | \([2]\) | \(967680\) | \(2.9051\) | |
13650.c2 | 13650q1 | \([1, 1, 0, -2230825, 1221557125]\) | \(628623316769266853/33232998629376\) | \(64908200448000000000\) | \([2]\) | \(483840\) | \(2.5585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13650.c have rank \(1\).
Complex multiplication
The elliptic curves in class 13650.c do not have complex multiplication.Modular form 13650.2.a.c
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.